Nonlinear static response analysis of sandwich beams using the Refined Zigzag Theory

The Refined Zigzag Theory (RZT) is assessed for the buckling and nonlinear static response analysis of multilayered composite and sandwich beams. A nonlinear formulation of the RZT is developed taking into account geometric imperfections and nonlinearities using the Von Kármán nonlinear strain-displacement relations. FE analyses are conducted employing C ⁰ -beam elements based on the RZT and the Timoshenko Beam Theory (TBT) to model three sandwich beams with different core materials and slenderness ratios, in both simply supported and cantilever configurations. The reference solutions are obtained by high-fidelity FE commercial codes, Abaqus® and Nastran®. The first two buckling loads are evaluated for the beams without initial imperfections. Several shapes are then assumed as geometric imperfections to calculate the beams’ nonlinear response to axial-compressive loads. The comparisons show the very high accuracy of the RZT (comparable to high fidelity FE commercial codes) for both the buckling and nonlinear static analyses and its superior capability with respect to the TBT to deal with sandwich beams with low slenderness ratio and higher face-to-core stiffness ratio.